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Substitute Numbers for Letters in Calculations With Brackets

In this worksheet, students will replace letters with numbers and carry out questions using the four number operations, with some calculations in sets of brackets. They must give their final answers as numbers not letters.

Which of the calculations below shows the correct way to convert the letters into numbers?

9 + (7 x 4)

7 + (9 x 4)

6 + (7 x 9)

Following on from the last question, let's work out the first step to solving the problem:

If A = 7, B = 9, C = 6 and D = 4, what is B + (A x D)?

Remember that when we have brackets in a question we solve the equation inside them first.

Can you find A x D first?

36

35

28

40

And now the final step to solve the problem:

If A = 7, B = 9, C = 6 and D = 4, what is B + (A x D)?

We know from the last question that (A x D) = 7 x 4 = 28.

Now complete the rest of the equation and write your answer as a number.

TRUE or FALSE?

When we see brackets in a maths problem, we must calculate the sum inside them first.

True

False

If a = 3, b = 7, c = 5 and d = 2, what is a + (b x c)?

Which of the calculations below shows the correct way to convert the letters into numbers?

7 + (5 x 3)

2 + (7 x 5)

3 + (7 x 5)

If a = 3, b = 7, c = 5 and d = 2, what is a + (b x c)?

What part of the equation should be answered first?

3 + 7

7 x 5

3 + 5

Let's put all the steps together now:

If a = 3, b = 7, c = 5 and d = 2, what is a + (b x c)?

Work out the answer to the full equation and record your answer as a number.

Following on from the last question:

If a = 3, b = 7, c = 5 and d = 2, what is a + (b x c)?

Which number are you adding a to?

35

40

38

36

Now you are going to be the examiner!

Three different students have been given the question below:

If A = 10, B = 4, C = 8 and D = 3, what is A + (B x D)?

Which students have answered the question correctly by creating the right calculation from the information given?

Following on from the last question, we will now find the final answer as a number:

If a = 10, b = 4, c = 8 and d = 3, what is a + (b x d)?

ANSWERS

Question 1

If A = 7, B = 9, C = 6 and D = 4, what is B + (A x D)?

Which of the calculations below shows the correct way to convert the letters into numbers?

CORRECT ANSWER

9 + (7 x 4)

EDDIE SAYS

The question tells us that B = 9, A = 7 and D = 4.
If we swap these numbers in for the letters, then B + (A x D) becomes 9 + (7 x 4).
Can you remember what to do when you see brackets in a calculation?

ANSWERS

Question 2

Following on from the last question, let's work out the first step to solving the problem:

If A = 7, B = 9, C = 6 and D = 4, what is B + (A x D)?

Remember that when we have brackets in a question we solve the equation inside them first.

Can you find A x D first?

CORRECT ANSWER

28

EDDIE SAYS

The question tells us that A = 7 and D = 4.
If we swap these numbers in for the letters, then A x D becomes 7 x 4.
When we multiply 7 by 4, we reach the answer of 28.
The first step to solving the problem is now complete! Let's move on to the next step...

ANSWERS

Question 3

And now the final step to solve the problem:

If A = 7, B = 9, C = 6 and D = 4, what is B + (A x D)?

We know from the last question that (A x D) = 7 x 4 = 28.

Now complete the rest of the equation and write your answer as a number.

CORRECT ANSWER

37

EDDIE SAYS

The question tells us that B = 9.
If we swap this number in for the letter in the rest of the equation, then B + (28) becomes 9 + 28.
When we add 9 and 28, we reach the answer of 37.
Were you able to complete the final step to reach the correct answer? Let's try another for some more practise...

ANSWERS

Question 4

TRUE or FALSE?

When we see brackets in a maths problem, we must calculate the sum inside them first.

CORRECT ANSWER

True

EDDIE SAYS

This statement is TRUE.
The brackets show us the part of the sum that needs to be worked out first.
If we do not do this and just calculate the sum from left to right, we will get a different and wrong answer.

ANSWERS

Question 5

If a = 3, b = 7, c = 5 and d = 2, what is a + (b x c)?

Which of the calculations below shows the correct way to convert the letters into numbers?

CORRECT ANSWER

3 + (7 x 5)

EDDIE SAYS

The question tells us that a = 3, b = 7 and c = 5.
If we swap these numbers in for the letters, then a + (b x c) becomes 3 + (7 x 5).
The brackets are very important - can you remember why?

ANSWERS

Question 6

If a = 3, b = 7, c = 5 and d = 2, what is a + (b x c)?

What part of the equation should be answered first?

CORRECT ANSWER

7 x 5

EDDIE SAYS

The brackets tell us which part of the calculation to work out first.
So we should calculate the sum in brackets first which is b x c.
The question tells us that b = 7 and c = 5.
If we swap these numbers in for the letters, then b x c becomes 7 x 5.

ANSWERS

Question 7

Let's put all the steps together now:

If a = 3, b = 7, c = 5 and d = 2, what is a + (b x c)?

Work out the answer to the full equation and record your answer as a number.

CORRECT ANSWER

38

EDDIE SAYS

We already know that we must calculate the bracket first, which gives us a sum of 35.
The question tells us that a = 3. If we swap that into the rest of the equation then a + (35) becomes 3 + 35.
When you add 35 and 3, we reach an answer of 38.
Great work putting all those steps together maths coder!

ANSWERS

Question 8

Following on from the last question:

If a = 3, b = 7, c = 5 and d = 2, what is a + (b x c)?

Which number are you adding a to?

CORRECT ANSWER

35

EDDIE SAYS

In the last question, we worked out that (b x c) needs to be worked out first.
We substituted the letters for numbers to get the sum 7 x 5.
If we multiply 7 by 5, we reach the answer of 35.
This needs to be added to a to reach the correct answer.

ANSWERS

Question 9

Now you are going to be the examiner!

Three different students have been given the question below:

If A = 10, B = 4, C = 8 and D = 3, what is A + (B x D)?

Which students have answered the question correctly by creating the right calculation from the information given?

CORRECT ANSWER

EDDIE SAYS

The question tells us that A = 10, B = 4 and D = 3.
If we swap these numbers in for the letters then A + (B x D) becomes 10 x (4 x 3).
We need to complete the calculation in brackets first, so the order we need to work in is 4 x 3 + 10.
So only the final student would reach the right answer!
How did you find being the examiner? Was it easy or hard to spot the students' errors?

ANSWERS

Question 10

Following on from the last question, we will now find the final answer as a number:

If a = 10, b = 4, c = 8 and d = 3, what is a + (b x d)?

CORRECT ANSWER

22

EDDIE SAYS

The question tells us that a = 10, b = 4 and d = 3.
If we swap these numbers in for the letters, then a + (b x d) becomes 10 + (4 x 3).
We must work out the brackets first so 4 multiplied by 3 is 12.
Then we need to add 10 to this total, so we will reach an answer of 22.
Did you put the steps together in the right order to reach the correct answer?

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